Towards accurate orbital-free simulations: A generalized gradient approximation for the noninteracting free energy density functional

For orbital-free ab initio molecular dynamics, especially on systems in extreme thermodynamic conditions, we provide an innovative pseudopotential-adapted generalized gradient approximation (GGA) functional for the noninteracting free energy. This is achieved by systematic finite-temperature extension of our recent LKT ground-state noninteracting kinetic energy GGA functional [Phys. Rev. B 98, 041111(R) (2018), 10.1103/PhysRevB.98.041111]. We test the performance of the functional first via static lattice calculations on crystalline aluminum and silicon. Then we compare deuterium equation of state results against both path-integral Monte Carlo and conventional (orbital-dependent) Kohn-Sham results. The functional, denoted LKTF, outperforms the previous best semilocal free energy functional VT84F [Phys. Rev. B 88, 161108(R) (2013), 10.1103/PhysRevB.88.161108], and provides modestly faster simulations. We also discuss subtleties of identification of kinetic and entropic contributions to noninteracting free energy functionals obtained by extension from ground-state orbital-free kinetic energy functionals.